Abstract—The biological motivated problem that we want to solve in this paper is to predict the new members of a partially known set of genes involved in specific disease (i.e. disease gene prioritization). In this problem, we are given a core set of genes (i.e. the queries) involved in the specific disease. However, the biologist experts do not know whether this core set is complete or not. Our objective is to find more potential members of this core set by ranking genes in gene-gene interaction network. One of the solutions to this problem is the random walk on graphs method. However, the random walk on graphs method is not the current state of the art network-based method solving bioinformatics problem. In this paper, the novel un-normalized graph (p-) Laplacian based ranking method will be developed based on the un-normalized graph p-Laplacian operator definitions such as the curvature operator of graph (i.e. the un-normalized graph 1-Laplacian operator) and will be used to solve the disease gene prioritization problem. The results from experiments shows that the un-normalized graph p-Laplacian ranking methods are at least as good as the current state of the art network-based ranking method (p=2).

Index Terms—Graph, p-Laplacian, ranking, disease gene prioritization.

Hieu Le is with the IC Design Lab at Hochiminh City University of Technology, Vietnam (e-mail: lehieu.ee@gmail.com).
Hoang Trang is with Ho Chi Minh City University of Technology, Vietnam (e-mail: hoangtrang@hcmut.edu.vn).
Loc Tran is with University of Technology, Sydney, Australia (e-mail: tran0398@umn.edu).
Linh Tran is with Portland State University, Portland (e-mail: linht@pdx.edu).